School Segregation Index Builds

Authors

Mateo Frumholtz

Sara Garcia

Published

July 24, 2024

Minnesota School District-Level Indices

Exposure Index (same as Interaction Index?)

Interaction Index

Interaction Index is a measure of…

\[Interaction = \sum_{i=1}^n \left( \frac{B_i}{B} \right) \left( \frac{W_i}{T_i} \right)\]

Where:

  • \(B_i\) is the number of students of a particular racial group in a school \(i\).
  • \(B\) is the total number of students of the same racial group in the entire district.
  • \(W_i\) is the number of White students in school \(i\).
  • \(T_i\) is the total student enrollment of the school district \(i\).
  • \(n\) is the number of schools in the district.

Isolation Index

Isolation index is a measure of…

\[Isolation = \sum_{i=1}^{n} \left(\frac{B_i}{B} \right) \left(\frac{B{_i}}{T_i} \right)\] Where:

  • \(B_i\) is the number of students of a particular racial group in a school \(i\).
  • \(B\) is the total number of students of the same racial group in the entire district.
  • \(T_i\) is the total student enrollment of the district \(i\).
  • \(n\) is the number of schools in the district.

Normalized Exposure Index

Dissimilarity Index

The Dissimilarity index is a measure of…

Dissimilarity index was calculated following Wang et al.’s, methods found here.

\[Dissimilarity = \frac{1}{2} \sum_{i=1}^{n} \left|\frac{b_i}{B} - \frac{w{_i}}{W} \right|\] Where:

  • \(b_i\) is the number of students of a particular racial group in school \(i\).
  • \(B\) is the total number of students of the same racial group enrolled in the district.
  • \(w_i\) is the number of white students in school \(i\).
  • \(W\) is the total number of white students enrolled in the district.
  • \(n\) is the number of schools in the district.

Information Theory Index Plot

Difference in Exposure to Free Lunch

CBSA-Level Segregation Indices

Exposure Index

Isolation Index

Isolation index is a measure of…

\[Isolation = \sum_{i=1}^{n} \left(\frac{B_i}{B} \right) \left(\frac{B{_i}}{T_i} \right)\] Where:

  • \(B_i\) is the number of students of a particular racial group in a school \(i\).
  • \(B\) is the total number of students of the same racial group in the entire district.
  • \(T_i\) is the total student enrollment of the district \(i\).
  • \(n\) is the number of schools in the district.

Normalized Exposure Index

Dissimilarity Index

The Dissimilarity index is a measure of…

Dissimilarity index was calculated following Wang et al.’s, methods found here.

\[Dissimilarity = \frac{1}{2} \sum_{i=1}^{n} \left|\frac{b_i}{B} - \frac{w{_i}}{W} \right|\] Where:

  • \(b_i\) is the number of students of a particular racial group in school \(i\).
  • \(B\) is the total number of students of the same racial group enrolled in the district.
  • \(w_i\) is the number of white students in school \(i\).
  • \(W\) is the total number of white students enrolled in the district.
  • \(n\) is the number of schools in the district.

Information Theory Index

Difference in Exposure to Free Lunch

Index Selection